Having two ceremonies is generally frowned upon by the Church (although, I’m sad to admit, you will find Catholic pastors out there who “do their own thing” and allow it).
One option that no one seems to think of is asking for dispensation from the form of marriage (i.e., a Catholic wedding is supposed to be in a Catholic church building and presided by a priest or deacon). You can literally ask for that requirement to be dispensed with, and when that is granted, you can have a wedding that’s valid in your Christian community (which means it can be presided over by a non-Catholic minister, and in an environment outside of a Catholic church building).
Here’s the catch, though: when you go that route, you can’t have a Catholic cleric preside, and you can’t have the ceremony in a Catholic church building. (Some Catholics would try to mix-and-match – a Catholic cleric outdoors, or a non-Catholic inside a Catholic church building… and the Church won’t give you permission for that).
But, if all that you’re looking for is a wedding that’s valid in the Church, then what you’re looking for is one single ceremony – either according to Church form, or one that’s been dispensed from the requirement of form – then that’s absolutely possible!
“One ceremony that looks like my tradition and one ceremony that looks like yours” isn’t the route that the Catholic Church would be good with, though. The marriage ceremony is the marriage ceremony. You can’t have a “do-over” in a second environment.